In a sentence, search in iPhoto 9 (from iLife 11) is pitiful.
iPhoto Help specifically says you can search on phrases, but from what I can tell:

iPhoto always matches any word in the search field, making searching for more than one word impossible.
Even then, iPhoto's search results include many photos that have none of the search terms in the name, description or Place.

That combined with iPhoto 9's very lame implementation of the description field makes me very sad.

I wonder if Aperture or Lightroom would be better in this respect.

"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs

More on iPhoto.
Here's a replacement for the capability of copying and pasting edits that iPhoto 8 had.
I haven't used this, being constitutionally opposed to paying for features removed from software I've already paid for. Grr.

FeroXsoft's iPhoto Batch Enhancer 3.1.1 makes it possible to apply settings from the iPhoto Effects palette and Adjust palette to a batch of selected photos with just a few clicks. This release adds support for Mac OS X 10.7, support for batch processing while iPads, iPhones, cameras, or memory cards are attached, some fixes for iPhoto '11, and other changes. iPhoto Batch Enhancer is $20 for Mac OS X 10.4 and up (Universal Binary), including Snow Leopard, with iPhoto 5 or later.

"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs

Here is perhaps a related issue. Digital cameras label images they take with a unique number/letter code and those identifiers are transferred to iPhoto when the images are downloaded. For example, my camera transfers a photo called DSC5118 to iPhoto. I can give that photo a name (e.g., the name of the person or thing in the image) but the photo still retains that number in the iPhoto database. I have always found it ULTIMATELY FRUSTRATING that when you have a photo renamed in this way, that on one level iPhoto does not really know the picture by YOUR name, but instead, (and secretly) thinks that the photo is actually DSC5118. But to make this frustration complete... you cannot SEE the DSC identifier anywhere! You can "Get Info" on the photos in iPhoto but this little detail is concealed somewhere. If you know how to reveal this info... share it here on the Forum. I learned that you can SEARCH for that DSC5118 string and iPhoto will magically produce the correct photo. But there is no way that you can browse these numbers or see them listed until you search for the specific one you need. Aaarrrrghhhh!!! I have always found iPhoto to be a dumbed-down but mostly functional piece of fluff.

In the older versions of iPhoto, you could show extended photo information. In iPhoto 9, that's folded into the info panel. But not all the extended info available is viewable there. As you say, the actual document name is one of the bits of information that you can't see in the info panel. You could see it in the old versions. [Bad programmer. Go to your room!]
That info is still available to iPhoto search. Try this: copy the photo name, as it came from the camera, and paste in TextEdit. Now change the name in iPhoto. You won't see the camera number anywhere in iPhoto. But if you search on that camera number, you will find the photo.

I always leave my photos titled with the camera number, for that very reason. I put any other info in the description field--which the new version of iPhoto has also screwed up.

BTW, here's a workaround for this particular problem that I found buried on this Apple Discussion thread.
Select the individual photo, in the Photos view. Drag directly to the Preview icon on the Dock. In Preview, select Tools > Show Inspector. The filename will be in the General tab, no matter what the iPhoto "title" field has been changed to. BTW, there's also most, if not all, of the EXIF data available in the Info tab. A benefit is that no copy of the image is made.

By the way, here's another tip:

If you take a lot of photos, and/or use more than one camera, there will be several photos in your collection with the same camera number. You can come closer to uniquely identifying a photo by adding a month and day number to the camera number. For example, when I post a photo to bugguide.net or copy it to the Finder and use it on one of my websites, I identify the photo as follows, for example:
06114183.jpg, where 0611 is the month and year and 4183 is the camera number. At the very least, that narrows the search down to a tiny number of photos.

You could also come up with various other schemes.

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"Design is not just what it looks like and feels like. Design is how it works."
Steve Jobs